ORCHARD PARK, N.Y. -- There might not be a more difficult game this season for the Buffalo Bills than this Sunday's trip to the Atlanta Falcons' sparkling new home of Mercedes-Benz Stadium.

Under the NFL's rotating scheduling formula, the Bills play the Falcons -- and the rest of the NFC South -- every four years. Those games alternate between home and road sites, so the Bills' trip to Atlanta's $1.5 billion venue should have come after the Bills hosted the Falcons in Buffalo in 2013.

That never happened. Four years ago, the Bills and Falcons met at Rogers Centre in Toronto in what became the final installment of a once-per-season series that was unpopular with Buffalo's fans and players. As the NFL continues its expansion of its presence in London, the Bills' brief foray into Canada has largely been forgotten.

Jerry Hughes recorded a sack of Matt Ryan when the Bills last played the Falcons on Dec. 1, 2013, in Toronto. Timothy T. Ludwig/USA TODAY Sports

Finding players in the Bills' locker room who remember what it was like to play in Toronto is an increasingly difficult task. Only five players -- center Eric Wood, defensive tackles Marcell Dareus and Kyle Williams, offensive tackle Cordy Glenn and defensive end Jerry Hughes -- remain on the roster from the 2013 season. The organization is on its third coach, Sean McDermott, since that game, as well as its second general manager, Brandon Beane.

It is also under different ownership. When the Bills announced their Toronto initiative in 2008, then-owner Ralph Wilson spoke of Buffalo's economic hardship at the time compared to the growth of Canada's largest city. Fueling the fears of Buffalo's fan base, Wilson said he could not speculate as to whether the once-per-year game would eventually evolve into relocating his franchise to Toronto from Buffalo, where he founded it in 1960.

Wilson's move north backfired. Despite Buffalo's relative proximity to Toronto -- the cities are 100 miles apart by car -- Bills fans were generally resistant to the idea of traveling to a different city to watch their team play. Ticket prices were considerably higher, and the atmosphere in the domed Rogers Centre was stale compared to the outdoor environment at Ralph Wilson Stadium.

"A lot didn't work," Wood said last week in the Bills' locker room. "From a competitive standpoint, losing one of your home games is huge. When we would go up there, a lot of opposing fans would see it as a destination game. The high ticket cost, a lot of that deterred Buffalo fans from going. Really, at times, it put us at a disadvantage.

"I distinctly remember trying to run offense against the Bears up there [in 2010], and we ended up having to go with a silent count, after an offsides penalty. So from a competitive standpoint, it just didn't make sense. I know monetarily it made a lot of sense for the organization, so I definitely respect them for making a move for the betterment of our team."

Bills fullback Patrick DiMarco was a member of the Falcons in 2013 when he made his first trip to Canada for the game.

"It was a different atmosphere," he said last week. "You were playing in a baseball stadium where field conditions probably weren't the best. ... I remember driving in, and you saw some random jerseys. Just NFL fans in general. It was cool to see that. But it was noticeable when we were on offense how loud Bills fans were."

After the original five-year agreement ended in 2012, the Bills extended the deal to hold games in Toronto for another five seasons. The Bills lost to the Falcons in overtime 34-31 on Dec. 1, 2013. With attendance declining to a series-low 38,969 for that game, the 2014 trip to Toronto was canceled on March 5, 2014. Less than three weeks later, Wilson died at age 95.

In October 2014, the team was sold to Terry and Kim Pegula. The couple outbid a Toronto-based group that included Maple Leaf Sports & Entertainment chairman Larry Tanenbaum, who had been one of Wilson's business partners for the Toronto series. The Pegulas, who made a commitment to fans to keep the Bills in Buffalo, asked players for their input on playing one game each season north of the border, and Wood was among those who advised against it.

On Dec. 3, 2014, the Bills officially terminated their contract to play games in Toronto, closing a chapter of the team's history that is part of the memories of a dwindling few in the locker room.

Williams, who has played 11 full seasons in Buffalo without experiencing the postseason, still laments that the Bills not only gave up one of their home games but also let warm-weather teams such as the Dolphins and Falcons off the hook by playing late-season games in Toronto's dome instead of the biting chill of Buffalo's open-air home venue.

"You want every advantage you can get," he said last week. "That was giving away an advantage."